I store my 3 Corvettes, including my 2002 Z06, for a minimum of 6 months each year. I do everthing I can to prepare them for storage so that I only have to check the oil level and air pressure and do a general visual inspection when I remove them from storage. It usually takes about 6 to 8 hours per Corvette. You did not list all of the things that you did before storing, so I can't really comment on everything, but have some general suggestions. I do agree with the above posts that flatbedding the Z06 to the dealer is not necessary unless you suspect or find a problem. I would start the car, let it run for awhile, check for leaks and idle response, then make decisions on what must be done. A good chevy dealer can change out your fluids using the BG systems for anitfreeze, brake, clutch and power steering fluids. They can also remove the gasoline from the tank system. The dealer can place the Z06 on a lift and look at the drive shaft seals and axle gear housings; they can also check the oil pan for leaks. You may want to change these out if you have high mileage. Check your tires for cracks and then drive the Z06 to determine if the flat spots, if any, go away. I never put my Corvettes on blocks so that I do not stress the suspension. I have never had flat spots. Since you have a 2002, the fuel filter should be replaced - it is located outside of the fuel tank. Also, as stated above, get the fuel out of the tank as soon as possible, either be driving of syphoning. Then get fresh fuel (top tier) into the tank and run the engine. You may want to add some Techron 20 to the tank to start internal cleaning. Change the oil and the filter. Also, inspect your weatherstripping; apply weatherstipping grease to it to soften it. Check your hoses and belt. If the serpentine belt has cracks in it, replace it at your first opportunity. If the hoses are defective or leaking, replace them. Also, wash and wax the enterior, clean and lubricate the seats, vinyl and door hinges. Lubricate the hinges on the hood and trunk struts. Clean the carpets. Run thru all of your electrical components, and check the DIC for codes. Make sure your fob works (you may need a new battery). Check all of your lamps. Look at the condition of the shocks for leaks and test them by pushing down on the bumpers, they should rebound to the set position without additional movement. You could have your A/C checked also, but run it first and monitor it to see if it continues to cool the air.
I hope this helps, and it will be appreciated if you report back to us on anything you find after you remove the Z06 from storage. Will be a good reference to others. And as Jane Ann says, thanks for serving. You are a first class hero in my book.
Barrett